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    Kernel stable and uniquely generated modules
    (Publishing House of the Romanian Academy, 2021) Şahinkaya, Serap; Quynh, Truong Cong
    A module theoretic notion of annihilator-stable rings is defined and some characterizations of it are studied. A module M is called kernel-stable if every element α ∈ End(M) satisfies the following condition: if α(M) + Kerβ = M, β ∈ End(M), then (α − γ)(m) ∈Kerβ for an automorphism γ of M and for all m ∈ M. For a pseudo-semi-projective module M, this notion is equivalent to that of uniquely generated module. © 2021, Publishing House of the Romanian Academy. All rights reserved.